Valuing Credit Risk - Variance Reduction Techniques for Monte Carlo Methods

Master's Thesis from the year 2003 in the subject Mathematics - Applied Mathematics, grade: 2,0 (B), Frankfurt School of Finance & Management, language: English, abstract: This paper deals with the valuation of credit risk derivatives on the basis of MonteCarlo simulation methods with the main viewpoint on variance reduction techniques. Therefore, first an overview on credit risk derivatives like credit default swaps and firstto default baskets is given. It turns out that modelling of the joint distribution ofdependent credit default times proves to be the crucial element. Once obtained, anycredit derivative can be valued. A convenient way of achieving this is by use of thecopula concept, which migrates marginal distributions of credit default times obtainedfrom a credit curve into a joint distribution incorporating any kind of desired dependencystructure. A section devoted to this concept provides the necessary backgroundand properties. Next, the general Monte Carlo concept is introduced in detail and carefullyadapted to the valuation of credit derivatives, following the path of constructingdependent uniform random variables from dependent normal random variables. At thesame time, first insight is gained in the field of variance reduction which is intensifiedin chapter four, where a series of techniques including antithetic sampling and controlvariates is presented. The main focus shall lie from there on on importance sampling. In order to increase the efficiency of Monte Carlo methods, sampling is restricted to theregion of importance where the function to be evaluated - here: the indicator functionof the credit default times - does not vanish. This technique is applied and examinedin detail in the final chapter for the one- and multi-credit case. Exponential as well asnormal importance sampling densities are derived.